Homework Help:
Impulse/momentum/collision question

basically a cue ball is struck by a cue, and that ball travels (without friction) and hits another ball (which isnt moving initally). they give all the masses and the impulse of the cue hitting the first ball. they tell us its an elastic collision.

2. Relevant equations

p=mv
I=change in momentum

3. The attempt at a solution

ok its easy to get the initial speed of the first ball using the impulse/momentum equation. and i know since its frictionless the ball doesnt change speed.

so basically a ball hits a 2nd ball (both have the same mass)...how do you mathematically find the final speed? i know the 2nd ball will have the same velocity as the first one but how do you show it in equations?

momentum: (initials) m1v1 + m2v2 = (finals) m1v1 + m2v2

the first v2 is 0 (2nd ball isnt moving) and all the masses cancel but you only get:

v1i = v1f + v2f

if you use conservation of kinetic energy you get basically the same thing (only the v's are squared).

what do you do with that since the only thing we know (out of 3 variables) is the initial velocity of the first ball?

(also couldnt we assume it was elastic since the two balls didnt stick together?)

basically a cue ball is struck by a cue, and that ball travels (without friction) and hits another ball (which isnt moving initally). they give all the masses and the impulse of the cue hitting the first ball. they tell us its an elastic collision.

2. Relevant equations

p=mv
I=change in momentum

3. The attempt at a solution

ok its easy to get the initial speed of the first ball using the impulse/momentum equation. and i know since its frictionless the ball doesnt change speed.

so basically a ball hits a 2nd ball (both have the same mass)...how do you mathematically find the final speed? i know the 2nd ball will have the same velocity as the first one but how do you show it in equations?

momentum: (initials) m1v1 + m2v2 = (finals) m1v1 + m2v2

the first v2 is 0 (2nd ball isnt moving) and all the masses cancel but you only get:

v1i = v1f + v2f

if you use conservation of kinetic energy you get basically the same thing (only the v's are squared).

what do you do with that since the only thing we know (out of 3 variables) is the initial velocity of the first ball?

(also couldnt we assume it was elastic since the two balls didnt stick together?)

when the 2 balls don't stick, the collision could be elastic or inelastic, depending on whether any energy is lost during the collision. In a perfectly (ideal) elastic collision, such as is given in this problem, energy is conserved as well as momentum. Conservation of energy gives you a second equation, which will allow you (with some difficulty) to solve the 2 unknowns v1f and v2f.

conservation of energy may be quite bothering. You can use another method. Since collision is elastic, the bodies have the same speed of separating as that of approaching.see http://en.wikipedia.org/wiki/Coefficient_of_restitution
this means,
v2(f)-v1(f) = v1(i)
now you have two equations in two variables. solve them